Problem: Solve for $x$ and $y$ using substitution. ${-3x-2y = 9}$ ${y = 6x-12}$
Solution: Since $y$ has already been solved for, substitute $6x-12$ for $y$ in the first equation. ${-3x - 2}{(6x-12)}{= 9}$ Simplify and solve for $x$ $-3x-12x + 24 = 9$ $-15x+24 = 9$ $-15x+24{-24} = 9{-24}$ $-15x = -15$ $\dfrac{-15x}{{-15}} = \dfrac{-15}{{-15}}$ ${x = 1}$ Now that you know ${x = 1}$ , plug it back into $\thinspace {y = 6x-12}\thinspace$ to find $y$ ${y = 6}{(1)}{ - 12}$ $y = 6 - 12$ $y = -6$ You can also plug ${x = 1}$ into $\thinspace {-3x-2y = 9}\thinspace$ and get the same answer for $y$ : ${-3}{(1)}{ - 2y = 9}$ ${y = -6}$